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Deriving Identities

Date: 08/26/98 at 09:09:06
From: Marie McLean
Subject: Deriving Identities


I hope you can help me with a problem I can't seem to figure out.  

I'm supposed to derive the identity for sin 3x in terms of sin x.

I was told to use the identity for sin(a+b) on sin(2x + x) as a first 
step. I tried that and I was able to get further but I keep doing 
something wrong.

I would appreciate any help.

Date: 08/26/98 at 11:30:14
From: Doctor Rick
Subject: Re: Deriving Identities

Hi, Marie -

How far were you able to get? How do you know you did something wrong 
- do you know what the answer should be? If so, it's possible your
answer is correct but that you need to apply a trig identity to get it 
in the form you expect.

If you write the formula for sin(2x + x) and substitute the formulas 
for sin(2x) and cos(2x) where the latter appear in the formula, you 
should get an expression that has sin(x) and cos(x). You can eliminate 
the cos(x) and get it in a nice form by using cos^2(x) = 1 - sin^2(x).

- Doctor Rick, The Math Forum   
Associated Topics:
High School Trigonometry

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